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arXiv · 2605.28958

Quantum State of a Gravitating Region

Raphael Bousso·Sami Kaya·Guanda Lin·Arvin Shahbazi-Moghaddam
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Abstract

We propose that any compact $d$-manifold with elliptic data, $\mathcal{J}$, prepares a quantum state $|\mathcal{J}\rangle$ on its $(d-1)$-boundary $\sigma$. Elliptic data consists of metric and field values, or their conjugates, but not both. No asymptotic structure is required. Inner products and traces are evaluated by the gravitational path integral with closed boundary conditions obtained by gluing elliptic data manifolds. In particular, we give a prescription for the R\'enyi entropies $S_n$ of a subregion of $\sigma$. In a class of examples, we find that $S_n$ is nonnegative and nonincreasing with $n$, as required for consistency. We obtain the von Neumann entropy by analytic continuation and find agreement with the minimal surface prescription of Bousso and Penington.

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Raphael Bousso, Sami Kaya, Guanda Lin, Arvin Shahbazi-Moghaddam. 2026-05-27. Quantum State of a Gravitating Region. https://arxiv.org/abs/2605.28958

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